#### Answer

75$^{\circ}$F

#### Work Step by Step

Since May is represented by $x=4$, we substitute $x=4$ in the equation to find the value of $t$:
$t=60-30\cos\frac{x\pi}{6}$
$t=60-30\cos\frac{4\pi}{6}$
$t=60-30\cos\frac{2\pi}{3}$
$t=60-30(-\frac{1}{2})$
$t=60-15(-1)$
$t=60+15$
$t=75$
Therefore, the maximum afternoon temperature for the month of May is 75$^{\circ}$F.